(partial derivative)over-bar-dressing method for the coupled Gerdjikov-Ivanov equation

We apply the (partial derivative) over bar -dressing method to study a coupled Gerdjikov-Ivanov (GI) equation. Compared with results on the classical coupled GI equation, more general spatial and a time singular spectral problems associated with GI equation are derived from a local 2 x 2 matrix (partial derivative) over bar -equation via two linear constraint equations. A more general GI hierarchy with source is proposed by using recursive operator. The N-solitons of the coupled GI equation are constructed still based the (partial derivative) over bar -equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained. The results on the GI equation can be recovered from the conclusion given above as special reductions. (C) 2020 Elsevier Ltd. All rights reserved.